In typical baseband transmission systems that employ equalization techniques for equalizing channels with low-pass characteristics, a usable bandwidth extends from near DC up to a maximum frequency that is determined by a high-frequency roll-off of a communications channel and signal-to-noise (SNR) requirements of a receiver. Referring to FIG. 4, when a magnitude 310 of a channel response 324 is essentially a monotonically decreasing function of frequency 312, this limitation is straight forward and baseband signaling is able to utilize the full, usable bandwidth of the channel. For example, if a system has adequate SNR with up to 50 dB of channel attenuation then the channel whose magnitude 310 decreases monotonically at 41.6 dB/decade starting at 1 GHz could support baseband signaling over a 0-12 GHz band of frequencies.
It is not unusual, however, for a channel response 314 to include one or more significant notches, such as first notch 316, that result in a local minimum in the magnitude 310. Notches may be associated with reflections (due to differences in impedance, parasitic capacitance and manufacturing tolerances) and other non-idealities. At higher frequencies, the channel response 314 recovers substantially before finally dropping again due to the ultimately low-pass nature of the channel. For such channels, the use of baseband signaling, with a usable signaling bandwidth limited from near DC up to the first notch 316, does not take advantage of all of the usable transmission bandwidth. Additional unutilized bandwidth is available at higher frequencies where the channel response 314 recovers from the first notch 316. Reconsidering the previously described example with the channel response 314 having the first notch 316 in a notch band of frequencies 322 between 4 and 4.5 GHz, the system could only support baseband signaling over a first band of frequencies 318 between 0-4 GHz. A second band of frequencies 320 between 4.5 and 12 GHz, which has less than 50 dB of attenuation, cannot be used with baseband signaling due to the first notch 316. As a consequence, this usable transmission bandwidth is not used in the system. There is a need, therefore, for a signaling system that more effectively utilizes the available bandwidth for channels having low-pass characteristics with one or more significant notches.
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